The invention discloses a synthetic method of sitagliptin and a salt thereof. The synthetic method comprises the steps: carrying out an esterification reaction, a reduction reaction, an oxidizing reaction and a witting reaction on 2,4,5-trifluorophenylacetic acid as a starting raw material to obtain 4-(2,4,5-trifluorophenyl)-2-ethyl crotonate; then carrying out a hydroamination reaction on 4-(2,4,5-trifluorophenyl)-2-ethyl crotonate and chiral amine in the presence of butyl lithium or hexamethyldisilazane sodium to form a chiral hydroamination product; carrying out an esterolysis reaction, a condensation reaction and a hydrogenation reaction to obtain sitagliptin. The raw materials used in the synthetic method of sitagliptin are low in price and easy to obtain; the synthetic method of sitagliptin is less in step, easy to operate and capable of effectively reducing cost. By the use of the method, high-purity sitagliptin can be obtained, a sitgliptin phosphate obtained through salifying has an HPLC (High Performance Liquid Chromatography) and an ee (enantiomeric excess) value of more than 99% and can be applied to the field of medicine.